Details

sample115.0ms

Algorithm

intervals

Results

57.0ms	85×	body	1280	valid
27.0ms	61×	body	640	valid
7.0ms	74×	body	80	valid
6.0ms	25×	body	320	valid
2.0ms	11×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	39	10
2	67	10
3	153	10
4	439	10
5	1830	10
6	5001	10
done	5001	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
39×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
22×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`hypot-def`
8×	`add-exp-log` `associate-/r*` `sqr-pow`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 117

Calls

4 calls:

34.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
32.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
103.0ms	(pow (sin ky) 2.0)
102.0ms	(pow (sin kx) 2.0)
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify38.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	341	1065
1	1159	981
2	5001	976
done	5001	976

prune420.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.2b	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
0.2b	(/ (sin ky) (hypot (sin ky) (sin kx)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
18.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
10.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series517.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(hypot (sin ky) (sin kx))
229.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
171.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify138.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	287	725
1	1045	645
2	4962	644
3	5001	644
done	5001	644

prune272.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.2b	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
0.2b	(/ (sin ky) (hypot (sin ky) (sin kx)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
19.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
8.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series537.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(hypot (sin ky) (sin kx))
252.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
168.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify37.0ms

Counts

82 → 82

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	284	728
1	1150	648
2	5002	648
done	5002	648

prune253.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 9.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (hypot (sin ky) (sin kx)))
0.3b	(/ (sin th) (sqrt (hypot (sin ky) (sin kx))))
0.3b	(* (/ (sin th) (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
0.3b	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
84×	`times-frac`
61×	`add-cube-cbrt` `*-un-lft-identity`
51×	`sqrt-prod`
22×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
9×	`unswap-sqr`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 172

Calls

4 calls:

1.0ms	(sqrt (hypot (sin ky) (sin kx)))
9.0ms	(/ (sin th) (sqrt (hypot (sin ky) (sin kx))))
38.0ms	(* (/ (sin th) (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
9.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

series771.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(sqrt (hypot (sin ky) (sin kx)))
209.0ms	(/ (sin th) (sqrt (hypot (sin ky) (sin kx))))
246.0ms	(* (/ (sin th) (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
184.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

simplify64.0ms

Counts

184 → 184

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	552	2416
1	2357	2211
2	5002	2115
done	5002	2115

prune475.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 9.5b

regimes675.0ms

Accuracy

0% (0.4b remaining)

Error of 8.9b against oracle of 8.5b and baseline of 8.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	12	13
done	12	13

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.9s	2711×	body	1280	valid
744.0ms	1891×	body	640	valid
212.0ms	793×	body	320	valid
211.0ms	2308×	body	80	valid
56.0ms	297×	body	160	valid